My problem is that when I scale down my drawing, the line weights stay the same, blotting out the artwork. If I scale up, the line weights become too thin. I've noticed that parametric effects don't scale together with the drawing.

How do I scale drawings in Adobe Illustrator and still maintain the proportions of line weights, gradients, and effects such as offset path?

Another option is to select the object and go to Object > Path > Outline Stroke. Of course this is only for paths. And btw I would go with lawndartcatcher on this one, my proposal is just another option to have in mind.

Actually, it won't. If your line weights aren't scaling the lines won't scale - if you started with 1 px wide lines and you scale your drawing to 200% you'll still have lines that are 1 px wide (in other words, your lines will now be half the weight but twice the size).
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lawndartcatcherJun 10 '11 at 12:59